Eu vi esse problema no Quora e cheguei na resposta de 1/2, para qualquer 
tamanho de fila com n>=2. Achei muito interessante! Resolvi por recorrência e 
indução finita.

There are 100 people waiting in line to board an airliner with 100 seats.

The seats are numbered from 1 to 100. Each passenger holds a ticket with his 
seat number.

You are the last passenger in line.

One of the passengers ahead of you in line is crazy. We don’t know which one. 
He will ignore his seat assignment and sit in a random empty seat.

Every other passenger will sit in their assigned seat — unless it is already 
taken, in which case they too will sit in a random empty seat.

Passengers board one by one.

What is the probability that you will sit in your assigned seat?

EDIT for clarification: the crazy person might sit in his assigned seat; he is 
equally likely to sit in any open seat.

Link: What is your favorite math problem/puzzle? by John Coiner

-- msbrogli

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